# Which is longer 5 miles or 10 kilometers?

Nov 3, 2016

$10$ kilometers

#### Explanation:

$5$ miles is about $8$ kilometers, so $10$ kilometers is longer.

The exact conversion figure is $1.609344$, which follows from one inch being defined as $2.54$ cm

I find it handy to use the first few terms of the Fibonacci sequence as an approximation for converting between miles and kilometers.

The Fibonacci sequence starts $1 , 1$. Then every subsequent term is formed by adding the two previous terms:

$1 , 1 , 2 , 3 , 5 , 8 , 13 , 21 , 34 , \ldots$

The ratio of pairs of consecutive terms tends towards the Golden ratio $\approx 1.618034$, which is not too far off $1.609344$.

Hence we find $5$ miles is about $8$ kilometers, $8$ miles is about $13$ kilometers, etc.